Compactification of the Bruhat-Tits building of PGL by seminorms

We construct a compactification [inline-graphic not available: see fulltext] of the Bruhat-Tits building X associated to the group PGL(V) which can be identified with the space of homothety classes of seminorms on V endowed with the topology of pointwise convergence. Then we define a continuous map from the projective space to [inline-graphic not available: see fulltext] which extends the reduction map from Drinfeld’s p-adic symmetric domain to the building X.